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Birkhäuser - Birkhäuser Mathematics | Spectral Methods in Surface Superconductivity

Spectral Methods in Surface Superconductivity

Fournais, Søren, Helffer, Bernard

2010, XX, 324p. 2 illus..

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  • Covers groundbreaking results in the fast growing field of superconductivity
  • Provides a concrete introduction to PDEs and spectral methods
  • Covers both two- and three-dimensional cases of Ginzburg-Landau function extensively
  • Includes open problems
During the past decade, the mathematics of superconductivity has been the subject of intense activity. This book examines in detail the nonlinear Ginzburg–Landau functional, the model most commonly used in the study of superconductivity. Specifically covered are cases in the presence of a strong magnetic field and with a sufficiently large Ginzburg–Landau parameter kappa.

Key topics and features of the work:

* Provides a concrete introduction to techniques in spectral theory and partial differential equations
* Offers a complete analysis of the two-dimensional Ginzburg–Landau functional with large kappa in the presence of a magnetic field
* Treats the three-dimensional case thoroughly
* Includes open problems

Spectral Methods in Surface Superconductivity is intended for students and researchers with a graduate-level understanding of functional analysis, spectral theory, and the analysis of partial differential equations. The book also includes an overview of all nonstandard material as well as important semi-classical techniques in spectral theory that are involved in the nonlinear study of superconductivity.

Content Level » Graduate

Keywords » Ginzburg–Landau functional - Potential - functional analysis - magnetic fields - optimal elliptic estimates - parameter kappa - spectral theory - superconductivity

Related subjects » Birkhäuser Engineering - Birkhäuser Mathematics - Birkhäuser Physics

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